Epsilon Numbers and Cantor Normal Form
نویسندگان
چکیده
منابع مشابه
Epsilon Numbers and Cantor Normal Form
An epsilon number is a transfinite number which is a fixed point of an exponential map: ω ε = ε. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: ε0 = ω ↑↑ ω, εα+1 = εα ↑↑ ω, and for limit ordinal λ: ε λ = lim α<λ εα = α<λ εα. Tetration stabilizes at ω: α ↑↑ β = α ↑...
متن کاملYamabe Numbers and the Brill–Cantor Criterion
It is illustrated by a class of counter examples why the Brill– Cantor criterion is not sufficient to ensure the solvability of the Lichnerowicz equation for asymptotically flat, time reflection symmetric-free data.
متن کاملTypicality of normal numbers with respect to the Cantor series expansion
Fix a sequence of integers Q = {qn}n=1 such that qn is greater than or equal to 2 for all n. In this paper, we improve upon results by J. Galambos and F. Schweiger showing that almost every (in the sense of Lebesgue measure) real number in [0, 1) is Q-normal with respect to the Q-Cantor series expansion for sequences Q that satisfy a certain condition. We also provide asymptotics describing the...
متن کاملTrees, the Cantor set and the irrational numbers
The Cantor set, first described by Smith in about 1874, sits naturally as the limit points of the complete binary tree, showing that the Cantor set is homeomorphic to the topological power 2, where 2 denotes the discrete two-point space. It also illustrates why there is no topological change if we replace 2 here by a discrete n-point space for any n > 1. What if we replace 2 by N? Perhaps surpr...
متن کاملBadly Approximable Numbers and Vectors in Cantor-like Sets
We show that a large class of Cantor-like sets of Rd, d ≥ 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d ≥ 2. An analogous result is also proved for subsets of Rd arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2009
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-009-0032-8